Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Master Thesis in Finance
Spring 2012
Authors: Supervisor:
Amanda Kolobaric Jens Forssbaeck
Parisa Khatabakhsh
Performance of Hedge Funds in the
European Market
1
ABSTRACT
The aim of this paper is to investigate the performance of hedge funds during the period
between December 1999 and March 2012. We consider 8 different investment styles for the
European market. As it has been argued in several papers hedge funds differ from traditional
funds, since it allows for diversification and lower systematic risk. Previous studies show
inconclusive results regarding whether hedge funds are able to beat the market. In order to
find evidence for the existence of abnormal returns for the hedge funds we regress 3 different
asset pricing models, static CAPM, Fama-French three factor model and dynamic Multi-factor
model. In line with our expectations the Multi-factor model is better suited to capture the
dynamic risk exposures of the hedge funds since it includes additional risk factors as well as
instrumental variables, taking into account the effects of the business cycles. We investigate
the performance of the hedge funds in 3 different sub-periods and find that for some of the
investments strategies it is possible to obtain positive anomalies in returns. However, the
empirical results demonstrate that the number of significant alpha’s from the various models
change over time and strategies.
Keywords: Hedge funds, asset pricing models, Multi-factor model, investment strategies,
performance measures.
2
ACKNOWLEDGEMENTS
We would like to thank Professor Jens Forssbaeck for his guidance, responsiveness and on top
of all his valuable comments throughout this research process.
3
TABLE OF CONTENTS
1. INTRODUCTION .................................................................................................................. 5
1.1 Background .......................................................................................................................... 5
1.2 Problem Discussion .............................................................................................................. 6
1.3 Purpose ................................................................................................................................. 6
1.4 Limitations ............................................................................................................................ 6
1.5 Outline .................................................................................................................................. 6
2. THEORETICAL FRAMEWORK ......................................................................................... 7
2.1 Hedge Fund History ............................................................................................................. 7
2.2 Hedge Funds versus Traditional Investment Funds ............................................................. 7
2.3 Hedge Fund Definition ......................................................................................................... 8
2.4 Investment Strategies ............................................................................................................ 9
2.4.1 Directional Strategies ....................................................................................................... 9
2.4.2 Non-Directional Strategies ............................................................................................... 9
2.5 Previous Studies ................................................................................................................. 10
2.6 Asset Pricing Models .......................................................................................................... 12
2.6.1 CAPM .............................................................................................................................. 12
2.6.2 Fama-French Three Factor Model ................................................................................. 13
2.6.3 Conditional Factor Model ............................................................................................... 13
2.6.4 Risk Factors ..................................................................................................................... 14
2.6.5 Instruments ...................................................................................................................... 15
2.7 Performance Measures ...................................................................................................... 15
2.7.1 Jensen’s Alpha ................................................................................................................. 16
2.7.2 Sharpe Ratio .................................................................................................................... 16
2.8 Statistical Properties .......................................................................................................... 16
2.8.2 Autocorrelation ............................................................................................................... 17
2.8.2.1 Durbin-Watson statistics .............................................................................................. 17
2.8.3 Heteroskedasticity ........................................................................................................... 17
2.8.4 Multicollinearity .............................................................................................................. 18
2.8.5 Skewness .......................................................................................................................... 18
3. METHODOLOGY ............................................................................................................... 20
3.1 Motivation .......................................................................................................................... 20
3.2 General Method of Work .................................................................................................... 20
4
3.3 Data .................................................................................................................................... 21
3.4 Potential Biases .................................................................................................................. 22
4. EMPIRICAL RESULTS AND ANALYSIS ........................................................................ 24
4.1 Descriptive Statistics .......................................................................................................... 24
4.1.1 Multicollinearity .............................................................................................................. 26
4.2 CAPM ................................................................................................................................. 26
4.2.1 Results and Analysis ........................................................................................................ 27
4.3 Fama-French Three Factor Model .................................................................................... 29
4.3.1 Results and Analysis ........................................................................................................ 30
4.4 Conditional Factor Model .................................................................................................. 32
4.4.1 Result and Analysis ......................................................................................................... 33
5. CONCLUSION .................................................................................................................... 36
5.1 Further studies .................................................................................................................... 37
6. REFERENCES ..................................................................................................................... 38
7. APPENDIX .......................................................................................................................... 42
Table 7.1 Data statistics, first sub-period (December 1999 – December 2003) ........................................... 42
Table 7.2 Data statistics, second sub-period (January 2004 – December 2007) .......................................... 42
Table 7.3 Data statistics, third sub-period (January 2008 – March 2012) ................................................... 43
Table 7.4 Augmented Dickey-Fuller test for non-stationarity. ...................................................................... 43
Table 7.5 Results for Heteroskedasticity and autocorrelation for CAPM. .................................................... 44
Table 7.6 Results for Heteroskedasticity and autocorrelation, Fama-French Factor Model. ...................... 44
Table 7.7 Results for Heteroskedasticity and autocorrelation, Multi-Factor Model. ................................... 45
Table 7.8.Full conditional regression output for the entire period. .............................................................. 45
Table 7.9 Summarized Multi-Factor results for the entire period, December 1999 – December 2003. ....... 45
Table 7.10 Summarized Multi-Factor results for the entire period, January 2004 – December 2007. ........ 46
Table 7.11 Summarized Multi-Factor results for the entire period, January 2008 – March 2012. .............. 46
5
1. INTRODUCTION
In the introductory chapter we aim to provide the reader with the background of the topic, problem
discussion and specification on the current state of research which will constitute the foundation of the
purpose. In addition, limitations and comprehensive outline of the study will be presented.
1.1 Background
During the past two decades, we have seen 25 percent of growth in alternative investments
vehicles like hedge funds. With approximately 10 000 active hedge funds worldwide
estimated to be a $2 trillion industry (Hedge Fund Association), increasing their prominence
in the financial market and providing investors with opportunities to manage risks and achieve
absolute returns. Perhaps, mainly because of the beneficial features of hedge funds, unlike
mutual funds, containing low systematic risk due to its low correlation with traditional asset
classes as well as limited government oversight (Ackermann, C., McEnally, R., &
Ravenscraft, D., (1999), Liang, B. (1999), Agarwal, V., & Naik, N.Y. (2000)).
Despite the fact of recent focus on hedge funds, the alternative investment vehicle has been in
existence since the year of 1949 and can be attributed to Alfred W. Jones. As he created an
investment fund as a general investment partnership, he had the idea of a (non directional /
market neutral) hedge fund that involved taking a long position in undervalued assets and at
the same time taking short position in overvalued assets. This innovation enabled investors to
make large bets with limited resources by an effectively leveraged investment capital.
(Brown, S.J., Goetzmann, W.N., & Ibbotson, R.G., 1999)
In general, there have been evidence showing both positive (absolute) return and performance
persistence (Edwards, F.R., & Caglayan, M.O., 2001). Investing in mutual funds will on
average underperform passive investment strategies that typically don’t actively attempt to
profit from short term fluctuations. The basic idea of hedge funds is to reduce volatility and
risk, at the same time yield high absolute returns in both bull- and bear markets. Thus, by
employing different unconventional investment strategies will allow the hedge fund manager
to instantly adapt and benefit from the volatile market. (Agarwal, & Naik, (2000), Fung, W.,
& Hsieh, D.A., (2000), Edwards, F.R., & Caglayan, M.O., (2001)
6
1.2 Problem Discussion
With the intention of analyzing hedge fund performances the majority of previous studies
often use static/unconditional asset pricing models, such as CAPM and Fama-French three
factor model, ignoring the time variation and overall ignoring the changing state of economy.
The problem of these model have as a consequence shifted focus towards conditional models,
allowing for time variability in order to overcome problems associated with different
conditional models. However, as previous studies in the field have given numerous
inconclusive findings regarding hedge fund performance applying static models, we will
therefore consider a further throughout research in the field applying both unconditional and
conditional models. This is necessary from both academics as well as an investor’s point of
view, in order to both overcome these problems and finding whether hedge funds really do
add value in terms of return.
1.3 Purpose
The purpose of this paper is to investigate and contribute to our understanding of the
performance of European hedge funds given different hedge fund styles. With the intention of
finding whether it is possible to produce excess returns, we apply different performance
methods, both conditional and unconditional models.
1.4 Limitations
We conduct this investigation using data provided from Eurekahedge, based on a set of
currently active European hedge funds which covers the available data sample of returns
between December 1999 and March 2012, including two distress periods (IT-bubble and real
estate-bubble). We will consider the European region as one unit, as the European index
comprises funds that are allocated to Europe, rather than individual countries.
1.5 Outline
The following chapter will provide a presentation of relevant theoretical issues and empirical
findings. In chapter three, data selection and work procedure will be clarified and specified as
well as relevant asset pricing models in addition potential biases will be discussed. In the
fourth chapter we present and analyze empirical findings. The final chapter will contain the
most important conclusions and suggestions for further research in the field.
7
2. THEORETICAL FRAMEWORK
This chapter will explain the relevant theories. Firstly we will present historical background and
definition of hedge funds then followed by comparison to traditional investment vehicles. Additionally,
the reader will be given explanation of relevant past findings as well as asset pricing models,
performance measures and its risk factors and instruments. We conclude the chapter by reviewing
different statistical properties. The theoretical framework will stand as a good base for further
analysis of the empirical findings.
2.1 Hedge Fund History
The conception of a hedge fund goes back to the year of 1949, when Alfred W. Jones, an
Australian journalist, came to the idea of short selling the overvalued stocks and
simultaneously going long in undervalued ones. He found out that this investment style
known also as a market neutral strategy, would result in gaining profits no matter in which
direction the market moves. Thus, the returns would depend on investors’ skills in choosing
right stocks but not the overall market reactions. He used leverage to purchase more shares
and enhance the returns and at the same time stayed away from risk exposures by short
selling. This combination made his investment strategy conservative and reduced the effects
of the market movements. This market neutral strategy has been followed by most hedge
funds during 1970’s. Although the start was quit slowly, the numbers of the hedge funds rose
up quickly during 1990’s which also resulted in various investment strategies. (Brown,
Goetzmann, & Ibbotson, 1999)
2.2 Hedge Funds versus Traditional Investment Funds
According to empirical studies, there are several differences between hedge funds and mutual
funds. In contrast with traditional investment vehicles, due to their numerous investment
styles the systematic risk is lower for the hedge funds as they allow for diversification. Hedge
funds’ limited regulations facilitate the investment decision making for their managers,
meanwhile the special fee structure gives incentive to the managers to perform more in line
with investors’ interests compared to the mutual funds. In contrast with traditional funds, the
fee depends on the performance rather than size of the asset. Additionally, due to its higher
water mark, the fee is only achievable when the managers make up the previous losses which
can be counted as another motivation. Diverse return targets can also be considered as another
difference between these two types of funds. Hedge funds are absolute performers while on
the other hand mutual funds are relative performers as their performance judge against
benchmarks like S&P 500 index. All in all, most of the times hedge funds show better
performance than mutual funds. (Liang, 1999)
8
Another difference is the restricted availability of the hedge funds. Mutual funds are easily in
the access of all groups of people with different wealth level, whilst hedge funds are only on
hand for special group of investors with higher wealth. It is possible to make money out of
hedge funds even at the time of down market, since its performance is regardless of the
market’s movement. Fund managers’ personal investment in the hedge funds is more common
compared to the traditional funds. Besides, their measurement for performance differs, since
the successful mutual fund has to outperform the market index whereas the success of the
hedge fund relies on the higher return due to its risk exposures. (Anderlind, P., Eidolf, E.,
Holm, M., Sommerlau, P., 2003)
2.3 Hedge Fund Definition
The meaning of hedge funds commonly refers to a general limited investment partnership.
The word hedge stems from protecting your investments with the objective of mitigating risk
exposure and making absolute returns on their underlying investments from market
uncertainty, i.e. generating positive returns in both up and down markets (Brown, Goetzmann,
& Ibbotson, 1999). Hedge funds are of interest to both academics as well as investors due to
their return profiles that significantly differs from mutual funds (Fung & Hsieh, 2000).
However, with a minimum investment ranging from $250,000 to $10,000,000 or more, hedge
funds can undertake any financial instrument and non-traditional trading strategies
(directional- and non-directional) unlike other funds, hence allowing for diversification
opportunities. For this reason we have seen a steady growth of 25 percent in alternative
investment vehicles like hedge funds, meaning that both the number and capital controlled
have increased their prominence in the financial market. However, as a result of the rather
limited regulation, it is with difficulty to say how many active hedge funds really exist, as
there are no regulations of having publicly available information regarding the operations of
alternative investments like hedge funds. Currently, there approximately exist 10 000 reported
active hedge funds worldwide and the number is growing every day, estimated to be a $2
trillion industry (Hedge Fund Association). According to Anderlind et al. (2003) 80 percent of
the active hedge funds are located in US, 13 percent in UK, 4 percent in Asia and remaining 3
percent in Europe. Even if the European hedge fund market is still fairly small as well as new,
it is still regarded as the market with the highest current growth rate compared to others.
(Anderlind et al., 2003)
9
2.4 Investment Strategies
We will closer investigate 8 hedge fund strategies. In line with Agarwal and Naik (2000) we
separate the different strategies according to whether they are directional, non-directional or
miscellaneous.
2.4.1 Directional Strategies
Strategies with high correlation with the market utilize the market movements and are referred
as directional:
Long Short Equities: This investment style focuses on short selling the equities that are
overvalued and expected to decrease in value and buying long undervalued securities that are
likely to have increase in value. By this investment strategy the market risk can be neutralized
and it can produce optimal risk-adjusted returns. This style is a combination of three strategies
long equities, short equities and modest leverage.
Macro: This is a very elastic strategy since it is used in various markets that are expected to
give the best opportunities. This investment style is a combination of leverage and long
positions which has an effect on securities, currency rates, commodities, fixed incomes and
interest rates. Appropriate timing is the key element for success in this investment style.
CTA/Managed Futures: This strategy is known as Commodity Trading Advisors. This
strategy combines long and short positions in order to yield returns in both up- and down
markets. The funds generally invest in currency markets plus options and futures.
2.4.2 Non-Directional Strategies
In the case of low correlation with the market, the classic market neutral strategy is classified
as non-directional:
Event Driven: Investment strategy that focuses on investing in situations where there is some
form of corporate activity or change i.e. exploring inconsistencies in the markets before/after
corporate events takes place, by taking a position in undervalued security that is expected to
rise in value due to the event. These corporate activities can refer to merger and acquisitions
(M&A), recapitalizations or liquidations to mention few (Agarwal & Naik, 2000). The main
risk is tied to the probability of event not occurring.
10
Fixed Income: By employing fixed income strategy, the hedge fund manager is able to earn
relative value and maximize its arbitrage opportunities by exploiting price anomalies between
fixed income securities and derivatives. According to Agarwal and Naik (2000) the risk of the
fund varies and depend on duration, credit exposure and leverage employed.
Arbitrage: An investment approach that involves buying a security or other financial
instrument in one market and simultaneously shorting a similar instrument in another market.
Hence, hedge managers can profit from price anomalies as a result of market inefficiencies.
Relative Value: It is an investment strategy that consists of managers simultaneously taking
long and short positions in related financial instruments that are expected to appreciate and
depreciate respectively, by doing so it allows investors to profit from the relative value of the
instruments.
In addition to the main categories a third category will be presented, Multi-Strategy as it can
be applied across the sub-groups:
Multi-strategy: This strategy is a combination of several investment styles such as convertible
bond arbitrage, long short equity, statistical arbitrage and merger arbitrage. This
diversification allows for lower volatility as well as smoother returns. These positive returns
are not dependent on direction of the market movements.
2.5 Previous Studies
During the last decades there have been a lot of researches done concerning hedge funds as a
result of their fast growth and the performance of the hedge fund is controversial according to
different studies. Some investigators believe that hedge fund returns are worse than what have
been expected because of their several biases as well as their high fees (Malkiel & Saha
2005), while in contrast many of other studies show greater performance of hedge funds
compared with mutual funds.
Liang (1999) investigated the performance of hedge funds for a period of 5 years, starting
from January 1992 until December 1996. In line with Fung and Hsieh (1997), Liang (1999)
argue that an investor holding a hedge fund portfolio will gain more than the one holding a
traditional mutual fund portfolio, since the hedge fund allows for diversification among
11
different strategies which don’t have high correlation with each other. On the other hand, the
compensation of mutual fund is related to the fund size while the fee of the hedge fund
depends on its performance. According to his findings, hedge funds present higher Sharpe
ratios as well as lower betas which consequently results in a greater performance compared
with the traditional mutual funds.
Ackermann, McEnally and Ravenskraft (1999) studied the performance of the hedge funds
considering return, risk and managerial incentives from 1988 to 1995. They compared hedge
funds with both mutual funds and standard market indices and conclude that while hedge
funds do better than the former they still don’t outperform the latter. They explained the
superior performance of the hedge funds by referring to several characteristic such as their
elastic investment styles and enticement fees as well as less governmental regulation.
Brown, Goetzmann and Ibbotson (1999) analyzed the performance of the offshore hedge
funds in US as a representative of the industry since the offshore funds consist of the most
important hedge funds. By applying unconditional CAPM, they found the evidence for lower
average annual return as well as lower standard deviation of the offshore hedge funds
compared to S&P 500 index, for the same period as Ackermann, McEnally and Ravenskraft
(1999). Their empirical study resulted in finding positive risk-adjusted returns for offshore
funds measured by Jensen’s alpha and Sharpe ratios.
Edwards and Caglayan (2001) used monthly returns of eight different investment strategies
between January 1990 and August 1998. Their results signified the fact that the hedge funds
abnormal returns depend on the type of the investment styles. However, using conditional
multifactor models, only twenty five percent of the hedge funds of their sample provided
positive risk-adjusted excess returns measured by the significant estimated alphas. They also
found considerable performance persistence over one- and two year scopes. As they
mentioned in their article, managerial skills in addition to incentive payments of the hedge
funds could count as some reasonable explanations for their remarkable performance.
In line with Edwards and Caglayan (2001), Kat and Miffre (2003) applied multifactor models
in order to investigate the performance of the hedge funds during the period of 1990 to 2000.
However, in contrast with the results of Edwards and Caglayan (2001), more than three
quarter of the hedge funds in the sample yielded abnormal returns.
12
2.6 Asset Pricing Models
The factor models break down the return of the asset into different factors. These models
identify the risk factors and can be used to compute the sensitivities of the assets to these
factors. In general, factor models for asset returns are mostly used in order to decompose the
risk and return into reasonable components and estimate the anomalous returns of the assets.
They also measure the volatility of the returns as well as the covariance among them. These
models allow for predicting future returns in different situations.
2.6.1 CAPM
The one-factor Capital Asset Pricing Model, introduced by Sharpe, W. (1964) and Lintner, L.
(1965), implies that the security’s return can be explained adequately by the assets’ sensitivity
to the market portfolio (beta). This model also takes into account the market expected return
as well as the expected return of the risk free asset. Beta is the non-diversifiable risk which
calculates the riskiness of the asset compared to the market. The security will have more
volatility that the market if the beta is superior than one and vice versa. The higher the risk is
the higher the expected return will be.
CAPM is based on several basic assumptions. In this model the utility-maximizing investors
are risk averse and they only care about the variance and mean respectively as a measure of
risk and return. The information is the same among all the investors, implying homogenous
expectations. In other words, by using the same inputs, investors expect the same amount of
risk and return. Besides, asset prices take into account all the accessible public information
and rapidly adjust to the new information released in the market. The market is also assumed
to be complete i.e. there are no taxes and transaction costs, the prices are not affected by
investors and at the risk free rate limitless borrowing and lending is permitted. The portfolio
lies on the efficient frontier so it can be optimized by having the lowest possible level of risk
for its level of return. In order to analyze the performance of the hedge funds we consider the
excess returns yielded by the eight different strategies in Europe. Sharpe and Lintner (1964)
hence argue that if investors hold homogenous expectations, mean-variance efficient portfolio
and the markets are assumed to be complete, the portfolio will itself will be considered to be a
mean-variance efficient portfolio. We apply CAPM by running the OLS time series
regression:
13
Whereas Rit is the expected monthly return of each hedge fund’s investment style at time t, Rft
is the risk free rate (one month Treasury bill rate), Rmt is the return on the market portfolio, εt
represents the error term. α and β are regression parameters. We run the regression in terms of
excess returns (Rit – Rft) on the market risk premium, (Rmt – Rft). The beta coefficient stands
for the measure of risk. (Campbell, J.Y., Lo, A.W., & Mackinlay, A.C., 1997)
2.6.2 Fama-French Three Factor Model
In order to describe the stock returns, in contrast with one variable CAPM, Fama, E. and
French K.R. (1992) introduced the three factor model which was superior in explicating asset
returns over time. They discuss the fact that average returns are also related to other risk
factors such as size and book-to-market value, since the traditional asset pricing model’s risk
factor solely wouldn’t be able to capture these return anomalies. So as to investigate the
performance of hedge funds we use Fama-French three factor model:
β, γ and δ are counted as the factor sensitivities of returns. (Rm – Rf) is the market risk
premium. SMB, is the measure for the size premium and HML accounts for value- over
growth stocks (Fama & French, (1996), Ogden, J.P., Jen, F.C. & O’Connor, P.F, (2002)).
2.6.3 Conditional Factor Model
Ferson and Schadt (1996) state that in the case of having time varying mean and variance, the
unconditional CAPM and Fama-French three factor model are not reliable since they can’t
capture the dynamics. They investigated the performance of fund strategies in changing
economic conditions.
Conditional factor approach was proposed by Ferson and Harvey (1999) in order to allow for
time-varying parameters as linear functions of instruments. Such instruments or conditioning
variables could represent the different economic conditions such as business cycles. Ferson
and Harvey (1999) introduced the general framework for conditional factor models:
14
Where ri,t+1 is the stock return at time t+1, rp,t+1 is a vector of excess returns on the risk factor-
mimicking portfolios at time t+1, Zt is a vector on conditioning variables at time t, αit shows
the abnormal returns, b0i is the mean of conditional beta and βit is the coefficient of
conditional beta regarding Zt. Since b 1i is a fixed coefficient, the equation above demonstrates
a fixed linear relationship among betas and conditioning variables for any given portfolio. We
can reach the multi factor model by combining the formulas mentioned above:
In order to be able to capture the risk exposures of the hedge fund returns, in line with Ferson
and Schadt (1996), Gupta, Cerrahoglu and Daglioglu (2003) used conditional variables
approach rather than traditional models. Considering hedge funds’ dynamic investment
strategies and their high volatility over time, they argued that time varying regressions are
more appropriate for measuring the performance of the hedge funds. All things considered, it
seems that applying conditional factor models would be a better choice which facilitates
capturing the performance of the different hedge fund strategies.
As suggested by previous empirical studies, additional risk factors as well as instrumental
variables should be included to explain the variance of the model and to characterize the
behavior of expected returns. Connor, G. and Korajczyk, R. (1988) and Lehmann, B. and
Modest, D. (1988) argue that five risk factors are adequate amount of factors. Since their
study showed that including more than five risk factors didn’t affect the results significantly.
The regression model applied will be presented below:
2.6.4 Risk Factors
The motivation of using five risk factors in the conditional multi-factor model is as follows:
Rm-Rf The reason behind including the market factor as a source of risk is motivated
entirely by CAPM (Fama & French, 1993).
15
SMB: Liew, J. and Vassalou, M. (2000) argue that SMB captures innovations in
economic growth expectations and inflation. According to Fama and French
(1993) small caps are riskier than large caps and therefore will yield higher
absolute returns and are hence a proxy for the size risk.
HML: According to Fama and French (1993) the book-to-market ratio is related to
higher return and in line with Liew and Vassalou (2000) HML would capture
information that is relevant in predicting the economic growth.
MOM: The explanation of including MOM as a risk factor is utterly based on results
and recommendations from Carhart’s (1997), Liew and Vassalou’s (2000) and
Jegadeesh, N. and Titman, S. (1993).
MT: Previous studies have showed inconclusive findings regarding the managers
market timing ability (Chen, L., & Liang, B., (2007), Fung, H.G, Xu, W.E., &
Yau, J., (2002)).
2.6.5 Instruments
The instrumental variables included, is used as proxies for the overall market condition and
business cycles, as a way of capturing the time variability.
VIX: Similar to Whaley, R.E. (2000) we ought to include the volatility index.
IPI: As the European gross domestic product is reported quarterly, construction of
monthly values would create certain biases, we therefore choose to include
industrial productivity as a proxy for business cycles in Europe.
2.7 Performance Measures
With the purpose of estimating the performance of the hedge funds in Europe from December
1999 to March 2012, we use two distinguished performance measures, Jensen’s alpha and the
Sharpe ratio.
16
2.7.1 Jensen’s Alpha
Jensen’s alpha is the intercept of asset pricing models which shows the performance of the
returns. CAPM returns are risk-adjusted as they allow for all the riskiness of the assets. The
positive Jensen’s index is a sign for the existence of positive abnormal returns in other words
it indicates higher asset returns compared to risk-adjusted returns. If the alpha is equal to zero
we will have the standard CAPM.
2.7.2 Sharpe Ratio
The Sharpe index is a measure of risk premium per each unit of risk which shows the balance
between the taken risk and expected return on the asset. Comparing two assets, the one with
higher Sharpe ratio indicates higher return for the same level of risk.
This index is calculable from any series of returns even with the lack of extra information
about the sources of profitability. However, despite this advantage, for reliable results the data
should be normally distributed so anomalies such as skewness or kurtosis may cause some
problems for this ratio.
2.8 Statistical Properties
To enable reliable empirical conclusions we need to consider some statistical properties. In
regression analysis, when applying time series data one needs to find whether the data can be
considered as being valid. Generally, when applying OLS with the purpose of estimating
parameters it is essential to find the data to be BLUE (Best Linear Unbiased Estimator),
showing the lowest possible mean squared error (MSE). If tests signify autocorrelation and/or
heteroskedasticity within the regression, as a consequence the results will no longer be
considered BLUE. Hence adjustments of data will be needed in order to obtain efficient and
reliable estimators, otherwise confidence intervals and hypothesis tests will be ambiguous.
Further on, we will examine various statistical properties.
17
2.8.1 Stationarity
According to Brooks (2008) we ought to test the data for non-stationarity, in order to find out
whether we can reject the null of unit root, against the alternative hypothesis of stationarity.
We perform an Augumented Dickey-Fuller (ADF) test type and use the test-statistic,
following DF-critical values in additional to the probability, in order to find whether we can
reject the null or not.
2.8.2 Autocorrelation
Autocorrelation is related to the problem of residuals being serially dependent of each other.
As the presence of positive serial correlation violates the OLS assumption, we will have to
account for problems related to statistical tests not being valid and reliable due to misleading
standard errors. To facilitate the problem, we initially need to examine the presence of
autocorrelation which can be done by applying traditional tests like Durbin-Watson statistics.
2.8.2.1 Durbin-Watson statistics
In line with Durbin J. and Watson G.S. (1951) we test the null that the errors are serially
independent against the presence of first order autocorrelation. The test statistics is
et is the residual at time t. If d>1, this implies positive serial correlation, whilst d<3 shows
evidence of negative autocorrelation. The rule of thumb signifies that d=1 indicates no
autocorrelation.
2.8.3 Heteroskedasticity
When the variance of the errors are not constant and finite, var(et) ≠ σ2
this will be of concern
in the application of regression analysis, as the presence will make the statistical tests invalid
(Brooks, C., 2008). The case with heteroskedasticity will as a fact not imply biased OLS
estimators, but will involve biased residuals. Consequently, the data will provide deceiving
standard errors and our inferences might as a result not be correct. We use the statistical test
called the White test in order to establish whether the residual variance is constant, var(et)=σ2.
Thus, we test the null of no heteroskedasticity against the presence of heteroskedasticity
18
(White, H., 1980). If the auxiliary regression analysis demonstrates that the dataset contains
heteroskedastic residuals one needs to apply the heteroskedastic-consistent covariance matrix
estimator in order to ensure unbiased residuals by adjusting the p-values.
2.8.4 Multicollinearity
When there is a relationship between two or more independent variables in a multiple
regression one might say that the regression suffers from multicollinearity. An important
statistical issue that is tied to the problem with collinearity and needs to be considered, is
related to spurious regressions. In order to identify this problem we will apply a correlation
matrix between all the explanatory variables, according to Brooks (2008) a correlation
coefficient in the range of 80% has to be considered. As a possible remedy Brooks (2008)
suggests one to exclude the variable that hold the highest level of correlation.
2.8.5 Skewness
The skewness is referred to the third standardized moment of a random variable and defined
as:
In order to detect the distribution of the hedge fund returns, one needs to take into
consideration the skewness. It is a measure of the asymmetry of the probability distribution of
stochastic variable. For left-skewed or left-tailed distribution, the skewness is negative and
vice versa. (Gujarati, D., 2006)
2.8.6 Kurtosis
Similar to skewness, kurtosis is another measure which describes the shape of the probability
distribution. However, unlike with skewness, this measure is based on the fourth moment of
the return data. Kurtosis can clarify the fatness of the distribution’s tails. The fourth
standardized moment minus 3 is defined as excess kurtosis which is used as an adjusted
version of kurtosis.
19
The formula indicates that for a normal distribution, the excess kurtosis should be zero so the
kurtosis would be three. Positive excess kurtosis means that the distribution has fatter tails and
higher peaks around the mean. This is also known as leptokurtic distribution while on the
other hand a platykurtic distribution with negative excess kurtosis contains thinner and lower
peaks around the mean. (Gujarati, 2006)
2.8.7 Normality
In order to check whether the returns have normal distribution, the Jarque-Bera test is
applicable. This test checks if the skewness and kurtosis of the data is close to a normal
distribution. The null hypothesis tests out whether skewness and excess kurtosis are jointly
equal to zero in other words if the sample returns are normally distributed. For the normally
distributed data, JB has a chi-squared distribution with two degrees of freedom.
20
3. METHODOLOGY
The following chapter will clarify and motivate the data selection process and the general method of
work in addition to specifying the chosen risk factors, pre-determined conditioning variables and
conclude the chapter with potential biases.
3.1 Motivation
As the objective for this research is to evaluate the performance of different hedge fund
strategies throughout different market conditions, we are therefore aiming to investigate
whether hedge fund managers are capable of producing excess returns. Furthermore, we use
quantitative data and empirically testing eminent performance models following a deductive
approach, i.e. by starting with hypothesis and then collect empirical data in order to find
whether we can reject or not reject our hypothesis and thereon draw conclusions. In line with
Jacobsen D.I. (2002) and Halvorsen K. (1992) we believe that the deductive approach is the
best suited and seem logical for the purpose of the investigation as well as to capture the
concepts of reality.
3.2 General Method of Work
To begin with, we collect our data sample from diverse databases during the period between
December 1999 and March 2012 consisting of 148 monthly observations for 8 different hedge
fund investment styles, with the motivation of being able to capture the excess returns in both
down- and up markets as we include both IT bubble as well as real-estate bubble. We
transformed the price index into returns with the following formula:
We obtained the monthly excess returns by taking the difference between Ri and the one
month T-bill, Rf. The excess returns are then estimated using Ordinary Least Squared (OLS)
against various independent variables. The estimations are performed on CAPM, Fama-
French Three factor model and a Conditional Multi-factor model which allows for time-
variability. Additionally, we test whether the data suffers from autocorrelation and
heteroskedasticity. In order to improve the OLS regression, we apply the Newey-West
estimator to adjust for autocorrelation and heteroskedasticity (HAC).
21
3.3 Data
The theoretical population corresponds to all the European countries, as indices are more
precise we believe that using the equally weighted index tracking the Europe industry would
be sufficient to capture the reality. The data sample is brought from different sources
including the Eurekahedge database where we found 148 monthly returns (net of all fees)
observations for 8 hedge fund styles since December 1999, to ensure a sufficient number of
consecutive observations to test some of the theories discussed. Other sources include
Thomson Reuters DataStream and Kenneth R. French data library.
Since neither daily nor weekly return data were available, the motivation of using monthly-
instead of annual returns, apart from giving more observations, enables us to track the hedge
fund return fluctuations more closely as well as enhances the accuracy of the standard
deviations. (Ackermann, McEnally, & Ravenscraft (1999), Brown, Goetzmann, & Ibbotson
(1999))
Further, we will present the sources of our risk factors and pre-determined conditioning
variables:
Ri: The return on 8 European hedge fund investment styles, including Arbitrage,
CTA/Managed Futures, Event Driven, Fixed Income, Long Short Equities,
Macro, Multi-Strategy, Relative Value and the data sample is obtained from
Eurekahedge.
RM: Is the market return on the whole stock market and used as a proxy for the
market (Fama & French, 2003). The data is obtained from Kenneth R. French
data library.
Rf: Stands for the risk free return rate (one month T-bill), collected from the
Kenneth R. French data library.
Rm-Rf Is consequently the excess return on the market.
SMB: Represents the spread in the returns between low-book-to-market stocks and
high-book-to-market stocks and constructed by forming value weighted
22
portfolios on size and BM (book-to-market) and measures the past excess
returns of small- over big caps. Data is obtained from the Kenneth R. French
data library.
HML: The data is obtained from Kenneth R. French data library and represents the
spread in the returns between high B/M and low B/M stocks. HML accounts for
the past excess returns of value- over growth stocks.
MOM: Momentum represents the difference between the average return on the portfolio
of past winners and portfolio of past loser.
MT: Is the market timing factor, max[(Rm-Rf)2, 0], the risk factor investigates if the
fund manager can account for the market timing ability, managers exhibiting
market timing ability will be able to earn higher abnormal returns when markets
are expected to rise and vice versa (Gupta et. al., 2003).
The pre-determined conditioning variables are:
VIX: The volatility index VSTOXX stands as a measure of the market’s perception of
risk and are designed to reflect market expectations of volatility in the European
equity market. The VIX-data is obtained from DataStream.
IPI: Industrial productivity measures the real production output and is used as a
proxy for business cycles in Europe. The data for industrial productivity is
monthly and given by DataStream. As the data for IPI exhibit seasonal
variation, for each month we use the average of the previous 12-months to
adjust and remove this cyclic variation.
3.4 Potential Biases
Whilst interpreting empirical results one needs to have potential biases in mind, as with
almost any base of data source there is a risk of hedge fund returns containing a variety of
biases that could affect the empirical findings.
23
Hedge fund research has confirmed the existence of a positive relationship between volatility
and fund disappearance (Ackermann, McEnally, & Ravenscraft, 1999). In general, when it
comes to survivorship biases we usually distinguish between surviving funds and defunct
funds. Whereas the surviving funds are still operating (alive) and present in the database as
opposed to defunct funds that have left the database (Fung, W., & Hsieh, D.A., (2000),
Malkiel, B., & Saha, A., (2005)). We are applying data from Eurekahedge, equal weighted
index for Europe. In order to eliminate the effects of survivorship they track down the
historical returns of funds that died and keep in the sample for the period they were alive as
well as including funds that are closed for further capital inflows.
Fung and Hsieh (2000) claim that selection biases might occur when return data are not
representative of the overall population, due to lack of regulations within the hedge fund
industry. Edwards and Caglayan (2001) argue that the selection bias that is caused by the
voluntary reporting might very well result in over- and underestimation of the hedge fund
performance, possibly affecting the returns both positively and negatively. In contrast Fung
and Hsieh (2000) argue that if the bias exists at all, it’s probably very small.
Another potential bias, the so called multi period sampling bias refers to return history.
Conducting empirical tests, it is of great importance to have reliable data in order to enable
future predictions. To enable more accurate and reliable results from empirical testing, one
needs sufficient return data. According to Ackermann, McEnally and Ravenscraft (1999) and
in line with Edwards and Caglayan (2001) a minimum of 24 months of return history is
required, although, Fung and Hsieh (2000) argue that the effect of the usage of shorter return
histories is relatively small. Therefore we believe that 148 months (per hedge fund style)
return data is sufficient in order overcome potential bias related to sample history.
24
4. EMPIRICAL RESULTS AND ANALYSIS
In the chapter we will present our empirical findings and analyze the results from the different asset
pricing models. To begin with, we will discuss some descriptive statistics, followed by analysis of
results which will be separated according to the different asset pricing models.
4.1 Descriptive Statistics
Before we start to investigate the performance of the hedge funds it is relevant to check for
the explanatory statistics of the hedge fund returns data for all the 8 different investment
strategies during the whole period.
In order to compare the hedge fund’s performance with the equity market we found it
appropriate to use S&P Europe 350 index as a proxy for the equity market since our data
sample consists of hedge fund returns in Europe. During the whole period of investigation, the
monthly average return for our sample hedge fund’s data is 0.465% which is remarkably high
compared to the monthly average return yielded by S&P Europe 350 index, -0.190% for the
same period. As it can be seen by the comparison between the standard deviations, 0.024 with
0.05, the average systematic risk for the hedge fund returns is much lower than for the equity
index. This is in contrast with our expectations about risk and return tradeoff since hedge fund
returns show higher return simultaneously lower standard deviation than the well-diversified
equity market index. Considering the data in the whole period, all the strategies yielded higher
monthly average returns than the S&P Europe 350 index. The lowest performance is for the
Arbitrage strategy while the Macro investment style shows the highest average return.
Strategies Average
return Std.
Sharpe
ratio Skewness Kurtosis JB
Arbitrage 0,046 0,019 -0,075 0,591 7,958 396,50
CTA 0,396 0,014 0,146 -0,553 3,395 78,07
Event Driven 0,432 0,020 0,125 -0,197 6,402 251,95
Fixed Income 0,212 0,018 0,014 -1,798 6,578 344,30
Long Short Equities 0,509 0,022 0,148 0,075 3,253 64,96
Macro 1,073 0,059 0,151 -0,022 2,522 38,96
Multistrategy 0,683 0,028 0,177 1,261 8,429 474,09
Relative Value 0,373 0,020 0,092 2,954 18,298 2264,48
S&P Europe 350 -0,190 0,051 -7,441 -0,717 3,596 14,78
Average of all hedge funds 0,465 0,025 0,097 0,289 7,104 489,17
Table 4.1. Data statistics for the whole period (December 1999 – March 2012).
25
The Sharpe ratio is a measure of risk premium per each unit of risk and for all the strategies
except for arbitrage, it outperforms the Sharpe ratio of the market equity index. The negative
Sharpe ratio for the Arbitrage strategy can be explained by its lower expected return than risk
free rate. According to this performance measure, we can conclude that the rational investor is
expected to invest in hedge funds due to their higher Sharpe ratio.
For almost half of the investment styles the skewness is positive which is more preferable for
the investors as it allows for gaining enormously high returns while at the same time limits the
downsides. As the data statistics shows (Table 4.1), the excess kurtosis indicates leptokurtic
distribution and the high Jarque-Bera test statistics for all the strategies following chi-two
distribution, is an evidence for non-normal distributed hedge funds data since it goes beyond
5.99 the critical value at 5% significance level.
We divided the whole period into three different sub-periods (1999M12-2003M12, 2004M01-
2007M12, 2008M01-2012M03). Except for the second sub-period, the hedge fund shows
better performance than the equity market index. Among all the investment strategies, Macro
in the first two sub-periods and event driven in the third one, show the highest return. The
average return of the hedge funds in the sub-periods before the financial crisis exceeds the
total period average (0.467%) while after the crisis sub-period’s return is significantly lower.
As the results shows (see Appendix, Table 7.1-3) the standard deviation in all the sub-periods
is almost twice higher for the equity market index compared with the hedge fund returns. So it
can be concluded that on average hedge funds face lower risk and in that case outperform the
S&P Europe 350 index. In contrast with the theory underlying CAPM, in all the sub-periods
but the one before the financial crisis, the lower risk followed by the higher return. Therefore
one can conclude that considering risk and return, the hedge funds outperforms the market in
both first and third sub-periods and it’s much safer to invest in the average hedge funds rather
than equity market. The higher Sharpe ratio for the well-diversified market index is also
another proof for the lower performance of the hedge funds for the sub-period II. For almost
half of the strategies, we can’t reject the null hypothesis of normally distributed sample data
in the second sub-period (lower JB test statistics than its critical value). Even though Jarque-
Bera test results imply that the errors are not normally distributed we still assume that the
estimators are consistent, which is in line with Brooks (2008).
Before we start to estimate the various equations, we also verify stationarity. We apply the
ADF test type (see Appendix, Table 7.4) and the results find the data to be stationary as we
26
are able to reject the null. As we include intercept in our estimations we can be sure that
E(ut)=0 holds. Test results of the remaining OLS assumptions will be discussed below, in the
end we believe that our parameters are BLUE, as the results and adjustments ensure the
validity of inferences made.
4.1.1 Multicollinearity
RM_RF SMB HML MOM MT VIX IPI
RM_RF 1
SMB 0,312 1
HML -0,140 -0,384 1
MOM -0,349 0,145 -0,124 1
MT 0,726 0,246 -0,128 -0,370 1
VIX 0,020 0,032 -0,235 -0,184 0,268 1
IPI -0,165 -0,112 -0,121 0,017 -0,191 -0,138 1
Table 4.2. Correlation between independent variables.
As a way of checking for multicollinearity between the independent variables we simply
examine the correlation matrix between each and one of variables. As discussed, a correlation
coefficient higher than 80 percent is considered to demonstrate problems related to
multicollinearity. Table 4.2, show that for all the independent variables the correlation doesn't
exceed the critical value of 80 percent, suggesting that we don't have problems with
multicollinearity.
4.2 CAPM
We are going to investigate whether the single beta unconditional asset pricing model, CAPM
is able to explain the performance of the hedge fund returns as the first stage of our empirical
research. As we mentioned before in the second chapter, we need to run the following model:
In order to be able to obtain reliable results we need to check for autocorrelation and
heteroskedasticity before explaining the Jensen’s alpha, CAPM beta and adjusted R-squared
as a measure of the goodness of the fit. The Durbin-Watson test statistic checks for the
existence of autocorrelation in the residuals. The value of the d-test statistic always lies
between zero and four. To test for autocorrelation the d-value should be compared with the
lower and higher critical values. The d=1 signifies no autocorrelation. So as a rule of thumb,
27
if the d-test statistic lies between one and three we can accept the absence of serial correlation
between the error terms while the values below one and above three will be signs of positive-
and negative autocorrelation respectively. Checking for the Durbin-Watson statistic for all the
hedge funds strategies in all the periods, none of the values specify autocorrelation problem in
our sample data. Moreover, with the aim of achieving BLUE coefficient estimates, we need to
check if the variance of the residuals in the regression model is constant and in other words
homoskedastic. White-test is used to test for the heteroskedasticity and the null hypothesis of
homoskedasticity can’t be rejected if the p-value is above 5% significant level. Considering
the p-values of the White’s F-statistics in all the periods, in the first period the fixed income
strategy, in the second period the CTA strategy and in the last period fixed income and
relative values strategies show the sign of heteroskedasticity with p-values lower than 5%. So
as to deal with this problem, we run the OLS regressions again this time by using the
heteroskedasticity robust standard errors. The results for Durbin-Watson test statistic and
white’s F-statistics for all the sub-periods are reported in the appendix (see Table 7.5).
CAPM
Strategies
Heteroskedasticity Autocorrelation
F-statistic P-value DW
Arbitrage 0,30 0,58 1,06
CTA 1,95 0,16 1,73
Event Driven 24,38 0,00 1,51
Fixed Income 13,55 0,00 1,49
Long Short Equities 0,03 0,85 1,31
Macro 0,14 0,71 1,75
Multistrategy 0,07 0,79 1,49
Relative Value 0,10 0,75 1,25
Table 4.3. Results for Heteroskedasticity and autocorrelation for
the entire period between December 1999 and March 2012.
4.2.1 Results and Analysis
The results for unconditional CAPM indicate that except for the last period, the majority of
the hedge funds strategies provided abnormal returns throughout the investigation. During the
whole period almost all the investment styles but arbitrage and fixed income, yielded positive
excess returns with regard to their significant positive Jensen’s alpha. In the first sub period,
excluding Fixed Income, all the strategies show significant positive intercept at level of 5
percent. In the second sub period only three strategies gained positive abnormal returns
whereas the Arbitrage strategy provided negative significant Jensen’s alpha. Multi-strategies
28
as well as the Long Short equities are the ones which showed positive excess returns in both
of these sub-periods. CTA is the only investment strategy which yielded positive anomalies
during the last period after the financial crisis. It is worth mentioning that there is no evidence
for the positive performance of any specific strategy in all sub periods.
CAPM
Strategies
1999m12-2012m03 1999m12-2003m12
Intercept Beta R2 Adj-R2 Intercept Beta R2 Adj-R2
Arbitrage 0,033 0,097 0,065 0,059 0,616 0,033 0,009 -0,013
p-value 0,83 0,002
0,029 0,523
CTA 0,387 0,067 0,055 0,048 0,795 0,096 0,086 0,066
p-value 0,001 0,004
0,002 0,076
Event Driven 0,400 0,228 0,336 0,331 0,257 0,022 0,028 0,007
p-value 0,024 0,000
0,014 0,252
Fixed Income 0,189 0,165 0,217 0,212 0,206 0,099 0,055 0,034
p-value 0,264 0,000
0,527 0,109
Long Short Equities 0,467 0,298 0,465 0,461 0,831 0,24 0,338 0,324
p-value 0,001 0,000
0,014 0,000
Macro 0,997 0,543 0,212 0,206 2,166 0,752 0,358 0,344
p-value 0,022 0,000
0,009 0,000
Multistrategy 0,651 0,228 0,164 0,158 1,421 0,066 0,01 -0,012
p-value 0,003 0,000
0,01 0,510
Relative Value 0,357 0,117 0,083 0,076 0,934 0,110 0,036 0,015
p-value 0,028 0,000 0,043 0,196
Table 4.4. Summarized CAPM results for the whole period and the first sub-period.
CAPM
Strategies
2004m01-2007m12 2008m01-2012m03
Intercept Beta R2 Adj-R2 Intercept Beta R2 Adj-R2
Arbitrage -0,427 0,046 0,017 -0,005 -0,087 0,167 0,182 0,165
p-value 0,002 0,384
0,784 0,002
CTA 0,095 0,004 0,000 -0,022 0,332 0,067 0,137 0,119
p-value 0,674 0,969
0,032 0,008
Event Driven 0,207 0,328 0,339 0,325 0,517 0,360 0,562 0,552
p-value 0,223 0,000
0,076 0,000
Fixed Income 0,045 0,157 0,199 0,182 0,268 0,216 0,511 0,501
p-value 0,697 0,002
0,202 0,000
Long Short Equities 0,554 0,400 0,350 0,336 -0,043 0,331 0,680 0,673
p-value 0,008 0,000
0,835 0,000
Macro 1,521 0,835 0,104 0,084 -0,613 0,368 0,332 0,318
p-value 0,099 0,026
0,196 0,000
Multistrategy 0,738 0,314 0,267 0,252 -0,313 0,347 0,646 0,639
p-value 0,000 0,000
0,179 0,000
Relative Value 0,17 0,130 0,169 0,151 -0,035 0,133 0,368 0,355
p-value 0,116 0,004 0,836 0,004
Table 4.5. Summarized CAPM results for the second and the third sub-periods.
29
For the whole period as well as all the three sub-periods Macro strategy yielded the highest
abnormal return, however for the last period the alpha is not significant. The observed alphas
were not significant for Fixed Income strategy in any sub-period even at 10 percent
significance level. The alphas vary across strategies from 0.2% to almost 2% throughout the
different sub-periods. Event driven yielded the lowest abnormal return of 0.25 percent per
month in the first period while the highest anomaly provided by Macro (2.16 percent) for the
same duration of time.
It is logical to expect very low betas for hedge fund returns, since by definition the
performance of these funds should be independent of the market movements. However,
obtaining factor loadings close to zero is unlikely in reality. Except for the first sub-period,
nearly all the betas are significant for all the investment styles. The beta differs from 0.066 for
CTA in the last sub period to 0.83 for Macro in the second sub-period. Throughout the entire
period the results didn’t show any negative factor loadings for any of the strategies.
According to R2 and adjusted-R
2, it seems that unconditional one factor asset pricing model,
CAPM is incapable of explaining the performance of the hedge fund returns. The values for
adjusted-R2 vary from -0.021 for CTA in the second period to 0.673 for Long Short equities
in the third period. It can be concluded that highest adjusted-R2 is obtainable for strategies
that are highly related to the equity market. However, in general low goodness of fit results
indicates the poor explanatory power of the model. CAPM doesn’t allow for inclusion of
other risk factors in the model so is not appropriate to capture the variability of returns of the
different of hedge funds.
4.3 Fama-French Three Factor Model
Secondly, we are interested in investigating another static model, named Fama-French three
factor model which have proven to outperform CAPM as it additionally includes both size-
and book-to-market risk factors. As presented in 2.6.2, we estimate the following equation:
Whilst estimating the equation, tests results from the DW and White’s-test implies that some
regressions suffer from both autocorrelation and heteroskedasticity (see Table 4.6, Appendix:
Table 7.6). Examining the Durbin-Watson statistics, we conclude that only arbitrage strategy,
in the period between 1999M12 and 2003M12, demonstrate problems related to
30
autocorrelation. Investigating the results obtained by the White’s tests, we find evidence for
heteroskedasticity in the period between 1999M12 and 2003M12 as well as for the whole
period since we reject the null of homoskedasticity. We adjust the data by employing the
Newey-West estimator.
Fama-French Model
Strategies
Heteroskedasticity Autocorrelation
F-statistic P-value DW
Arbitrage 24,97 0,00 1,08
CTA 0,74 0,53 1,79
Event Driven 5,76 0,00 1,56
Fixed Income 4,23 0,01 1,45
Long Short Equities 66,90 0,00 1,37
Macro 0,07 0,98 1,79
Multistrategy 1,01 0,39 1,52
Relative Value 106,93 0,00 1,24
Table 4.6. Results for Heteroskedasticity and autocorrelation for the entire period
between December 1999 and March 2012.
4.3.1 Results and Analysis
The Fama-French regression output for the whole period (Table 4.7) recording significant (at
5%-level) positive alphas within 4 out of the 8 strategies, implying that the different
alternative investment styles were able to “beat the market”. For the additional periods,
results show a declining number of significant alphas in both up- and down markets whereas
2, 3 and none significant alphas could be found for the first-, second- and third sub-periods,
respectively (Table 4.7-8). The strategies exhibiting significant alphas were also identified as
significant under the traditional asset pricing model. Regarding the alpha values, representing
the performance, one can conclude that the excess return decrease under the Fama-French
three factor model. A possible explanation of decreasing returns lies in the fact of additionally
including the risk factors that slightly reduce the excess returns as it better can explain the
variance. The significant alphas fluctuate and none of the strategies persistently exhibit
positive abnormal returns throughout the different periods. Merely all significant beta values
in the Fama-French three factor model were also shown to be significant under CAPM, except
of the beta value for the CTA-strategy in the first sub-period . During the investigation the
Event Driven-strategy displays the lowest significant market beta, except between 2004M01
and 2007M12, where Fixed-Income-strategy exhibit the lowest market beta. All the
31
significant betas were shown to be positively correlated with the overall market, regardless of
the market condition.
Fama-French Model
Strategies
1999m12-2012m3 1999m12-2003m12
Intercept Beta Beta-
SMB
Beta-
HML R2 Adj-R2 Intercept Beta Beta-SMB Beta-HML R2 Adj-R2
Arbitrage -0,015 0,085 0,068 0,037 0,081 0,061 0,727 -0,019 0,008 -0,103 0,074 0,011
p-value 0,950 0,031 0,271 0,448
0,112 0,687 0,924 0,136
CTA 0,323 0,051 0,088 0,050 0,101 0,082 0,339 0,162 0,183 0,227 0,330 0,284
p-value 0,006 0,033 0,009 0,140
0,173 0,002 0,001 0,001
Event Driven 0,332 0,226 0,046 0,094 0,362 0,349 0,123 0,039 0,056 0,064 0,165 0,109
p-value 0,062 0,000 0,242 0,063
0,261 0,070 0,015 0,028
Fixed Income 0,134 0,150 0,081 0,040 0,242 0,226 -0,016 0,096 0,139 0,065 0,133 0,074
p-value 0,442 0,001 0,023 0,354
0,964 0,174 0,065 0,490
Long Short Equities 0,405 0,271 0,125 0,018 0,504 0,494 0,715 0,196 0,134 -0,023 0,471 0,435
p-value 0,005 0,000 0,062 0,650
0,033 0,000 0,046 0,707
Macro 0,927 0,493 0,207 -0,031 0,230 0,214 1,564 0,784 0,321 0,226 0,401 0,360
p-value 0,037 0,000 0,107 0,808
0,085 0,000 0,085 0,333
Multistrategy 0,600 0,226 0,036 0,068 0,171 0,154 1,563 0,023 -0,025 -0,100 0,020 -0,047
p-value 0,007 0,000 0,571 0,284
0,014 0,849 0,842 0,529
Relative Value 0,381 0,116 -0,009 -0,039 0,087 0,068 1,147 0,072 -0,076 -0,115 0,053 -0,011
p-value 0,107 0,022 0,903 0,417 0,116 0,432 0,531 0,237
Table 4.7. Summarized Fama-French results for the whole period and the first sub-period.
Fama-French Model
Strategies
2004m01-2007m12 2008m01-2012m03
Intercept Beta Beta-
SMB
Beta-
HML R2 Adj-R2 Intercept Beta Beta-SMB Beta-HML R2 Adj-R2
Arbitrage -0,481 0,047 0,025 0,160 0,111 0,051 -0,076 0,175 -0,031 -0,011 0,183 0,130
p-value 0,001 0,470 0,731 0,039
0,821 0,008 0,832 0,928
CTA 0,143 -0,040 0,073 -0,047 0,012 -0,055 0,294 0,083 0,032 -0,099 0,197 0,144
p-value 0,552 0,724 0,388 0,620
0,059 0,006 0,635 0,073
Event Driven 0,161 0,291 0,107 0,220 0,430 0,391 0,486 0,416 -0,046 -0,217 0,606 0,580
p-value 0,342 0,001 0,253 0,025
0,093 0,000 0,714 0,037
Fixed Income -0,072 0,211 -0,059 0,234 0,409 0,369 0,281 0,246 -0,070 -0,078 0,534 0,504
p-value 0,505 0,000 0,319 0,000
0,182 0,000 0,315 0,296
Long Short Equities 0,530 0,322 0,189 0,247 0,452 0,415 -0,032 0,372 -0,085 -0,113 0,704 0,685
p-value 0,011 0,002 0,090 0,032
0,878 0,000 0,358 0,127
Macro 1,386 0,628 0,538 0,873 0,179 0,123 -0,703 0,463 -0,019 -0,416 0,417 0,379
p-value 0,144 0,172 0,299 0,104
0,132 0,000 0,925 0,014
Multistrategy 0,713 0,283 0,084 0,146 0,304 0,257 -0,291 0,407 -0,133 -0,159 0,691 0,671
p-value 0,001 0,006 0,451 0,205
0,202 0,000 0,192 0,053
Relative Value 0,198 0,084 0,088 0,017 0,209 0,155 -0,099 0,166 0,043 -0,189 0,513 0,481
p-value 0,083 0,126 0,156 0,785 0,521 0,000 0,387 0,000
Table 4.8. Summarized Fama-French results for the second and the third sub-period.
32
Most of the hedge funds have positive exposure to the size factors, however SMB coefficients
are not significant, apart from CTA- and Fixed Income strategies in the first sub-period and
CTA-, Event Driven- and Long Short Equity strategies in sub-period two, hence show
positive factor loading which is in line with previous studies (Fama & French, 1993).
The estimated book-to-market factors imply that some of the HML coefficients are significant
in period I, II and III. As value stocks impose higher risk, they should as a result generate
higher returns (Fama & French, 1993). Consequently, we would expect positive HML factor
loadings in up markets (period II) and negative in down markets (period III). The negative
sign imply shifts towards growth stocks which can be observed in last period, which doesn’t
come as a surprise given the financial crisis. The motivation of the different signs comes from
the fact that the market perceives the value stocks more risky over growth stocks (Table 4.7-
8).
Before going further investigating the unconditional models we briefly need to compare and
look at the explanatory power of the Fama-French factor model. The goodness-of-fit, R2,
indicates higher values of R2 than the traditional one factor model, in all periods, ranging from
8,1 percent obtained by the Arbitrage-strategy to 50,4 percent obtained by the Long Short
Equity strategy. We can for this reason conclude that the Fama-French factor model is better
in explaining the abnormal return compared to the traditional one factor model. Given that
hedge fund excess return variations are influenced by various risk factors, we will as a remedy
consider the conditional factor model, accounting for time variability will increase the
goodness-of-fit concerning the different strategies.
4.4 Conditional Factor Model
We extend our research in order to find more suitable model for explaining hedge fund risk
exposure and check whether it is possible to observe positive and significant alphas by
estimating the conditional Multi-factor model:
33
Hence, we extend the Fama-French three factor model, by adding the supplementary risk
factors, momentum and market timing. In addition we include instrumental variables that
incorporate market’s perception of risk, VIX, and the variable that stands as a proxy for the
overall market situation, IPI.
According to the DW-statistics we can come to the conclusion that not any of the regressions,
regarding any period, suffer from autocorrelation (Table 4.9, Appendix: Table 7.7). On the
other hand, when it comes to problems related to heteroskedasticity, for the whole period the
results of the White’s test implies that Arbitrage-, Long-Short Equities and Relative value
strategies suffer from heteroskedasticity, whereas Long-Short Equities also show problems in
the first sub-period. We simply solve this problem by applying the Newey-West estimator and
instead use the robust standard errors.
Multi Factor Model
Strategies
Heteroskedasticity Autocorrelation
F-statistic P-value DW
Arbitrage 5,91 0,00 1,56
CTA 1,17 0,31 1,77
Event Driven 0,97 0,49 1,58
Fixed Income 0,53 0,92 1,45
Long Short Equities 30,37 0,00 1,39
Macro 1,50 0,11 1,97
Multistrategy 1,07 0,39 1,54
Relative Value 24,57 0,00 1,41
Table 4.9. Results for Heteroskedasticity and autocorrelation for
the entire period between December 1999 and March 2012.
4.4.1 Result and Analysis
Under the Multi-factor model we find significant alphas for 3 out of the 8 strategies for the
period between end of 1999 and March 2012 and the first sub-period. For the second sub-
period we find positive significant alphas for 2 of 8 strategies and 1 of 8 for the last sub-
period implying that the majority of the alphas demonstrate non significance regardless of
period. Results reveal abnormal results ranging between -0.23% and 0.62% per month. Since
only 1 out of the 8 strategies demonstrate a negative insignificant alpha, we believe that hedge
funds as an alternative investment vehicle are able to hedge returns as results signify positive
alphas for the majority of the strategies (although some of them are insignificant). This
implies that they are able to generate positive excess returns in both up- and down markets.
34
Macro strategy demonstrates the highest significant abnormal return and also shows the
highest average return (Table 4.1) between December 1999 and March 2012, we consequently
believe that it is beneficial to invest in this hedge fund strategy.
Multi-Factor
Model
Strategies
1999M12 -2012M03
Intercept Beta Beta-
SMB
Beta-
HML Beta-MOM Beta-MT R2
Adj-
R2
Arbitrage -0,227 -3,414 0,740 -2,117 -0,660 6,948 0,327 0,249
p-value 0,437 0,000 0,631 0,035 0,343 0,002
CTA 0,528 -0,076 1,802 2,307 -0,838 0,084 0,243 0,157
p-value 0,012 0,896 0,033 0,016 0,111 0,940
Event Driven 0,220 -2,467 1,627 2,194 0,244 1,107 0,538 0,485
p-value 0,322 0,000 0,071 0,031 0,664 0,349
Fixed Income 0,322 -1,649 1,263 -0,154 0,167 1,784 0,361 0,288
p-value 0,173 0,014 0,185 0,885 0,778 0,155
Long Short
Equities 0,483 -1,410 2,600 -0,071 -0,733 2,439 0,596 0,550
p-value 0,028 0,034 0,021 0,945 0,258 0,102
Macro 2,341 0,117 2,842 -0,098 -2,418 3,891 0,363 0,290
p-value 0,003 0,958 0,368 0,978 0,222 0,350 Multistrategy 0,621 -3,502 -0,233 1,068 -1,343 3,783 0,257 0,171
p-value 0,125 0,002 0,886 0,561 0,189 0,079 Relative Value 0,287 -1,203 -1,345 0,558 1,161 4,059 0,226 0,138
p-value 0,268 0,070 0,388 0,606 0,184 0,135
Table 4.10. Summarized Fama-French results for the entire period, December 1999 – March
2012.
The market factor (Rm-Rf) observed for the various hedge funds, are significant (at 5%
significance level) in five cases (Table 4.10), where all are negative and imply that hedge fund
returns have a negative sensitivity towards the market movements and results show negative
significant betas for all the periods except for the second sub-period (see Appendix: Table
7.9-11). Theories suggests that in both way, hedge funds should enable positive returns no
matter market situation and as more the model is able to explain the variance, the results of
the market factor will tend towards 0.
The outcome referring to the negative and positive size factor loadings indicate that there are
strategies that take short positions and long position in small capital stocks respectively.
Hence, it’s evident that fund managers prefer small (large) caps over large (small) caps when
we have positive (negative) factor loadings for the SMB. The results show that the IT-bubble
did generate one negative size factor loadings for the arbitrage strategy, compared to results
given during- and after the real estate crisis. (see Appendix: Table 7.9-11)
35
Three out of the eight HML coefficients are significant (Table 4.10), whereas two of the
strategies show positive factor loadings. We cannot therefore explain whether hedge funds are
exposed to value risk and if preferences lean towards growth stocks, since only two of the all
show positive factor loadings.
Data sample stretching between December 1999 and March 2012 show that none of strategies
demonstrate significant momentum beta. Referring to period I and II we find that 1 and for
period III, 3 out of 8 strategies respectively show significant betas. On the other hand the sign
does vary, where the majority of the strategies show negative significant betas for the period
II and III, implying that momentum cannot be considered as a compensation of bearing an
extra risk, i.e. momentum can’t explain the abnormal returns.
Regarding the market timing ability, MT, the results show that only one out of all the
strategies (Arbitrage) in the whole period shows significant coefficient value while we get
positive significant betas for 3 and 2 of the strategies for the first and third sub-periods
respectively (see Table 4.10, Appendix: Table 7.9-11). The existence of positive market
timing ability is in line with Chen and Liang (2007). Meaning that, hedge fund managers in
deed are able to earn higher abnormal returns when the market is expected to rise, which is in
line with Gupta et al. (2003). However, according to our findings the small number of
significant coefficients implies that this cannot be verified.
The conditional effects in Table 7.8 (see Appendix) shows that the (IPI·Rm-Rf) is positive and
for the majority also significant. This implies that the market factor is higher in bear markets,
i.e. the hedge funds will follow the market more in up markets and less in down markets,
which seems logical. For the other conditional effects, a minor part of the betas are not
significant and for this reason we are not able to explain the various conditioning effects.
The goodness-of-fit, R2
and the adjusted-R2 of the conditional Multi-factor model indicates
that the explanatory power is significantly higher than for both CAPM and Fama-French three
factor model. The explanatory power has consistently risen, varying from 22% and 60%, the
results proves that the conditional Multi-factor model, including both additional risk factors
and instrumental variables provides the best fit compared to the static models, as it
significantly and consistent contribute to the models explanatory power.
36
5. CONCLUSION
In this last chapter we will summarize our main findings in addition we will bring a suggestion for a
potential further research.
The purpose of this paper has been to examine whether it is possible to obtain abnormal
returns with various European hedge fund strategies during the period between December
1999 and March 2012 and to identify the potential risk factors affecting the returns. In line
with previous studies on the performance of hedge fund, we applied unconditional CAPM,
Fama-French three factor model and a conditional time varying Multi-factor model. Jensen’s
alpha and Sharpe ratio have been used as measures of the performance.
CAPM Sign.
Alpha
Average
alpha
Average
R2
Average
adj. R2
Whole period 6 0,435 0,199 0,194
Sub-period I 7 0,903 0,115 0,096
Sub-period II 3 0,363 0,181 0,163
Sub-period III 2 0,003 0,427 0,415
Fama-French
Model
Sign.
Alpha
Average
alpha
Average
R2
Average
adj. R2
Whole period 4 0,386 0,222 0,206
Sub-period I 2 0,170 0,206 0,152
Sub-period II 3 0,322 0,263 0,213
Sub-period III 0 -0,017 0,481 0,447
Multi-Factor
Model
Sign.
Alpha
Average
alpha
Average
R2
Average
adj. R2
Whole period 3 0,572 0,364 0,291
Sub-period I 3 1,132 0,542 0,327
Sub-period II 2 0,403 0,513 0,284
Sub-period III 1 0,227 0,713 0,59
Table 5.1 Comparison between the three different model estimations.
According to the table, the summary of results show that some of the hedge fund investment
styles produce abnormal returns considering their significant alphas. This is similar to the
findings of Liang (1999), Edwards and Caglayan (2001) and Kat and Miffre (2003). Higher
Sharpe ratios for hedge fund returns compared with the Sharpe ratio of the market equity
index for most periods is also a proof of the fact that hedge funds can beat the market and
produce abnormal returns even though it varies among time and strategies. It is also evident
that the number of significant alphas obtained from the various models change over time. A
37
possible explanation could be due to the fact that manager’s ability to earn hedge fund returns
differs among various business cycles.
The goodness-of-fit consistently rise as we include additional explanatory variables to the
model, which was expected. R2
and adjusted-R2
show lower values for the CAPM and Fama-
French compared to the conditional Multi-factor model. Hence, both models appear to be
inappropriate to capture the performance of hedge funds as they are not able to explain the
dynamic risk exposures. Even thought the average goodness-of-fit of the conditional model is
not as high as we expected, it is still higher than 35 percent reported by Kat and Miffre
(2003). Another explanation of the poor goodness-of-fit can be attributed to the number of
explanatory variables and including insufficient risk factors.
5.1 Further studies
We believe that it could be a matter of interest to include supplementary risk factors as well as
instrumental variables as a proxy for the business cycles in order to enhance the explanation
power of the Multi-factor model. Furthermore, including other strategies as well as a more
specified group of countries such as eastern or western European countries would be relevant
to explore the existence of abnormal returns in the European markets.
38
6. REFERENCES
Ackermann C., McEnally R., Ravenskraft D. (1999) The Performance of Hedge Funds: Risk,
Return and Insentives. Journal of Finance, Vol.54, No. 3, 833-874.
Agarwal, V., Naik, N. (2000). Multi-Period Performance Persistence Analysis of Hedge
Funds. The Journal of Financial and Quantitative Analysis, Vol. 35, No. 3, 327-342.
Anderlind, P., Eidolf, E., Holm, M., Sommerlau, P. (2003). Hedgefonder. Academia Adacta,
Lund
Brooks, C. (2008). Introductory Econometrics for Finance. Cambridge University Press.
Brown, S. J., Goetzmann W. N., & Ibbotson R. G. (1999). Offshore Hedgefunds: Survival and
Performance 1989-1995. Journal of Business, Vol. 72, No. 1, 91-117.
Carhart M.M. (1997). On Persistence in Mutual Fund Performance. The Journal of Finance,
Vol.52, No 1, 57-82.
Campbell, J.Y., Lo, A.W. & Mackinlay, A.C. (1997). The Econometrics of Financial Markets.
Princeton University Press.
Chen, Y., & Liang, B., (2007). Do Market Timing Hedge Funds time the market?
Journal of Financial and Quantitative Analysis, Vol. 42, No. 2, 827-856.
Connor, G. & Korajczyk, R., (1988). Risk and Return in an Equilibrium APT: Application of
a New Test Methodology. Journal of Financial Economics, Vol. 21, 255-290.
Durbin, J., & Watson, G. S., (1951). Testing for Serial Correlation in Least Squares
Regression, II. Biometrika, Vol. 38, 159–179.
Edwards, F., & Caglayan, M., (2001). Hedge Fund Performance and Manager Skill. Journal
of Futures Markets, Vol. 21, No.11, 1003-1028
39
Fama, E., & French, K. (1993). Common Risk Factors in the Returns on Stocks and Bonds.
Journal of Financial Economics, 33, 3-56.
Fama, E.F. & French, K.R. (1996). Multifactor Explanations of Asset Pricing Anomalies. The
Journal of Finance, Vol. 51, No. 1, 55-84.
Ferson, W., & Harvey C. (1999). Conditioning Variables and the Cross Section of Stock
Returns. The Journal of Finance, Vol. 4, 132-135.
Ferson, W., & Schadt, R. (1996). Measuring Fund Strategy and Performance in Changing
Economic Conditions. Journal of Finance, Vol. 51, 425-462.
Fung, W., Hsieh, D. A. (1997a). Emprical Characteristics of Dynamic Trading Strategies: The
Case of Hedge Funds. Review of Financial Studies, Vol. 10, 275-302.
Fung, W., Hsieh, D. A. (2000). Performance characteristics of hedge funds and commodity
funds: Natural vs. spurious biases. Journal of Financial and Quantitative Analysis, Vol. 35,
291–307.
Fung, H.G., Xu, X.E., & Yau, J., (2002). Global Hedge Funds: Risk, Return and Market
Timing. Financial Analysts Journal, Vol. 58, No. 6, 19-30.
Gujarati, D. (2006). Essentials of Econometrics (3rd ed.). Singapore: McGraw-Hill.
Gupta, B., Cerrahoglu, B., & Daglioglu, A. (2003). Evaluating Hedge Fund Performance:
Traditional Versus Conditional Approach. The Journal of Alternative Investments, 7-24.
Jacobsen, D. I., (2002). Vad, hur och varför? Om metodval i företagsekonomi och andra
samhällsvetenskapliga ämnen. Studentlitteratur: Lund.
Jegadeesh, N. &Titman, S. (1993). Returns to Buying Winners and Selling Losers:
Implications for Market Efficiency. Journal of Finance, Vol. 48, 35-91.
40
Kat, H. M., & Miffre, J. (2003). Performance Evaluation and Conditioning Information:
The Case of Hedge Funds, Working paper. Faculty of Finance, Cass Business School, London
Lehmann, B. & Modest, D. (1988). The Empirical Foundations of the Arbitrage Pricing
Theory. Journal of Financial Economics, Vol. 21, 213-254.
Liang, B. (1999). On the Performance of Hedge Funds. Financial Analysts Journal, Vol. 55,
No. 4, 72-85.
Liew, J. & M. Vassalou (2000). Can book-to-market, size, and momentum be risk factors that
predict economic growth? Journal of Financial Economics 57, 221–245.
Malkiel, B., & Saha, A. (2005). Hedge Funds: Risk and Return. Financial Analysts Journal,
Vol. 61, No. 6, 80-88.
Ogden, J.P., Jen, F.C. & O’Connor, P.F. (2002). Advanced Corporate Finance – Policies and
Strategies. Prentice Hall.
Whaley, R.E. (2000). The investor fear gauge. Journal of Portfolio Management, Vol. 26, 12-
17.
White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct
Test for Heteroskedasticity. Econometrica, Vol. 48, 817-38.
DATA SOURCES
Eureka Hedge homepage: Indices. Available at: http://eurekahedge.com/indices/default.asp.
(Accessed: 25th
April, 2012).
Kenneth, R. French homepage: Data library – Fama/French Factors (including momentum).
Available at: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
(Accessed: 25th
April, 2012).
41
Datastream Advance Database, Thomson Financial Ltd. (MOM, MT, VIX, IPI, S&P Europe
350). (Accessed: 30th
May, 2012).
INTERNET SOURCES
The Hedge Fund Association. Retrieved from: https://thehfa.org/aboutus, (2012-04-20).
42
7. APPENDIX
Strategies Average Std. Sharpe
ratio Skewness Kurtosis JB
Arbitrage 0,600 0,019 0,185 2,659 12,612 241,34
CTA 0,748 0,018 0,280 -1,251 7,806 58,72
Event Driven 0,246 0,007 -0,010 -0,850 3,968 7,66
Fixed Income 0,157 0,023 -0,042 -1,523 6,616 44,71
Long Short Equities 0,712 0,022 0,206 1,646 9,306 101,19
Macro 1,794 0,068 0,227 -0,364 2,376 1,84
Multistrategy 1,388 0,036 0,313 2,025 9,182 109,25
Relative Value 0,879 0,031 0,201 2,264 9,842 134,65
S&P Europe 350 -0,864 0,057 -0,195 -0,409 2,618 1,63
Average of all hedge funds 0,816 0,028 0,170 0,576 7,714 87,42
Table 7.1 Data statistics, first sub-period (December 1999 – December 2003)
Strategies Average Std. Sharpe
ratio Skewness Kurtosis JB
Arbitrage -0,399 0,009 -0,779 -0,710 5,775 19,43
CTA 0,098 0,013 -0,141 0,229 3,514 0,95
Event Driven 0,409 0,014 0,095 -1,051 4,050 11,05
Fixed Income 0,142 0,009 -0,159 -1,028 4,082 10,79
Long Short Equities 0,800 0,016 0,316 -0,630 3,089 3,19
Macro 2,035 0,063 0,278 0,849 4,447 9,95
Multistrategy 1,931 0,015 1,117 -0,145 3,332 0,39
Relative Value 0,250 0,008 -0,038 0,839 3,354 5,88
S&P Europe 350 0,972 0,026 0,265 -0,584 2,437 3,36
Average of all hedge funds 0,658 0,018 0,086 -0,206 3,955 7,70
Table 7.2 Data statistics, second sub-period (January 2004 – December 2007)
43
Strategies Average Std. Sharpe
ratio Skewness Kurtosis JB
Arbitrage -0,056 0,024 -0,038 -0,497 6,165 23,38
CTA 0,345 0,011 0,278 -0,208 2,905 0,39
Event Driven 0,629 0,030 0,199 -0,245 5,018 9,17
Fixed Income 0,330 0,019 0,157 -1,852 8,755 99,51
Long Short Equities 0,042 0,025 0,003 -0,544 3,572 3,21
Macro -0,510 0,040 -0,138 -3,774 21,737 867,11
Multistrategy -0,214 0,027 -0,093 -0,821 3,770 6,99
Relative Value 0,012 0,014 -0,017 -1,679 7,182 61,13
S&P Europe 350 -0,649 0,060 -0,114 -0,483 2,915 2,00
Average of all hedge funds 0,072 0,024 0,044 -1,202 7,388 133,86
Table 7.3 Data statistics, third sub-period (January 2008 – March 2012)
ADF-test t-tatistic Prob
ri_rf_arb -6,81 0,00
ri_rf_cta -10,90 0,00
ri_rf_eve -7,75 0,00
ri_rf_fix -8,44 0,00
ri_rf_lon -8,06 0,00
ri_rf_mac -9,89 0,00
ri_rf_mul -5,46 0,00
ri_rf_rel -8,66 0,00
rm_rf -10,37 0,00
SMB -14,08 0,00
HML -11,32 0,00
MOM -11,67 0,00
MT -11,62 0,00
VIX_rm_rf -10,49 0,00
IPI_rm_rf -10,16 0,00
VIX_SMB -14,59 0,00
IPI_SMB -14,03 0,00
VIX_HML -10,71 0,00
IPI_HML -11,13 0,00
VIX_MOM -7,03 0,00
IPI_MOM -11,57 0,00
VIX_MT -10,20 0,00
IPI_MT -11,57 0,00
S&P -10,16 0,00
Table 7.4 Augmented Dickey-Fuller test for non-stationarity.
44
CAPM
Strategies
1999m12-2003m12 2004m01-2007m12 2008m01-2012m03
Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation
F-statistic P-value DW F-statistic P-value DW F-statistic P-
value DW
Arbitrage 0,67 0,42 1,04 1,91 0,17 1,50 0,14 0,71 1,31
CTA 3,57 0,07 1,75 7,70 0,01 1,64 1,43 0,24 1,82
Event Driven 1,18 0,28 1,51 0,69 0,41 1,48 1,52 0,22 1,79
Fixed Income 0,12 0,73 1,38 0,00 0,99 1,40 37,92 0,00 2,00
Long Short Equities 0,51 0,48 1,00 0,78 0,38 1,47 0,17 0,68 1,92
Macro 0,21 0,65 1,91 0,01 0,93 1,78 1,66 0,20 1,96
Multistrategy 0,95 0,33 1,56 1,45 0,24 1,94 0,19 0,67 2,01
Relative Value 0,51 0,48 1,27 0,01 0,94 1,52 28,49 0,00 1,59
Table 7.5 Results for Heteroskedasticity and autocorrelation for CAPM.
Table 7.6 Results for Heteroskedasticity and autocorrelation, Fama-French Factor Model.
Fama-French Model
Strategies
1999m12-2003m12 2004m01-2007m12 2008m01-2012m03
Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation
F-statistic P-value DW F-statistic P-value DW F-statistic P-
value DW
Arbitrage 95,63 0,00 0,94 0,78 0,51 1,74 0,62 0,61 1,30
CTA 1,29 0,29 1,87 3,12 0,04 1,66 1,20 0,32 1,94
Event Driven 0,76 0,52 1,64 1,05 0,38 1,76 1,08 0,37 1,68
Fixed Income 0,05 0,99 1,17 1,35 0,27 1,68 11,35 0,00 1,93
Long Short Equities 92,43 0,00 1,02 0,37 0,78 1,71 0,29 0,83 1,86
Macro 0,27 0,85 2,04 1,79 0,16 1,89 1,59 0,21 1,99
Multistrategy 0,49 0,69 1,57 0,47 0,71 2,01 0,24 0,86 1,90
Relative Value 37,74 0,00 1,29 1,38 0,26 1,56 7,65 0,00 1,59
Multi-Factor Model
Strategies
1999m12-2003m12 2004m01-2007m12 2008m01-2012m03
Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation Heteroskedasticity Autocorrelation
F-statistic P-value DW F-statistic P-value DW F-statistic P-
value DW
Arbitrage 1,80 0,08 2,07 1,16 0,35 1,80 0,78 0,69 1,70
CTA 0,73 0,74 1,94 0,84 0,63 1,91 0,65 0,81 1,91
Event Driven 0,31 0,99 2,21 0,51 0,92 1,62 0,53 0,91 2,09
Fixed Income 0,75 0,71 1,42 0,87 0,60 1,44 0,36 0,98 1,88
Long Short Equities 3,60 0,00 1,26 0,60 0,85 1,81 0,38 0,98 2,05
Macro 0,57 0,88 2,06 1,81 0,08 2,03 3,57 0,00 1,41
Multistrategy 1,03 0,46 1,33 0,78 0,69 2,16 0,30 0,99 1,89
Relative Value 0,69 0,78 1,62 1,19 0,33 1,37 0,14 1,00 1,83
45
Table 7.7 Results for Heteroskedasticity and autocorrelation, Multi-Factor Model.
Table 7.8.Full conditional regression output for the entire period.
Multi-Factor
Model
Strategies
1999M12 -2003M12
Intercept Beta Beta-
SMB
Beta-
HML Beta-MOM Beta-MT R2
Adj-
R2
Arbitrage 0,048 -1,936 -9,023 -1,886 2,469 4,068 0,633 0,461
p-value 0,912 0,000 0,012 0,002 0,549 0,005 CTA 1,020 -1,861 -1,091 -1,567 5,271 1,493 0,609 0,425
p-value 0,023 0,012 0,071 0,061 0,261 0,054 Event Driven 0,203 -4,124 -3,092 -5,530 2,283 7,252 0,511 0,282
p-value 0,291 0,190 0,241 0,132 0,271 0,036 Fixed Income 0,075 1,869 -7,366 0,753 1,857 -2,041 0,491 0,252
p-value 0,906 0,076 0,396 0,950 0,010 0,072 Long Short
Equities 0,859 6,104 6,588 7,581 0,730 1,708 0,690 0,545
p-value 0,002 0,568 0,148 0,201 0,891 0,250 Macro 4,092 5,424 5,145 9,622 1,381 -3,351 0,581 0,384
p-value 0,021 0,058 0,826 0,766 0,455 0,268 Multistrategy 1,641 -2,050 -1,433 1,387 -0,152 5,223 0,177 -0,208
p-value 0,205 0,922 0,416 0,954 0,991 0,816 Relative Value 1,121 1,191 1,391 2,033 3,332 4,637 0,644 0,477
p-value 0,128 0,317 0,889 0,882 0,671 0,001
Table 7.9 Summarized Multi-Factor results for the entire period, December 1999 – December
2003.
46
Multi-Factor
Model
Strategies
2004M01 -2007M12
Intercept Beta Beta-
SMB
Beta-
HML Beta-MOM Beta-MT R2
Adj-
R2
Arbitrage -0,475 -2,032 1,592 -4,674 -1,082 -0,132 0,444 0,183
p-value 0,069 0,463 0,628 0,126 0,551 0,972
CTA -0,245 5,060 4,607 -3,929 -3,143 -2,282 0,329 0,015
p-value 0,553 0,262 0,388 0,420 0,287 0,708
Event Driven 0,467 0,848 1,551 -2,650 -4,210 -5,962 0,708 0,571
p-value 0,114 0,788 0,678 0,440 0,048 0,171
Fixed Income 0,062 -1,268 0,582 2,106 -1,888 0,239 0,606 0,421
p-value 0,771 0,581 0,831 0,400 0,215 0,939
Long Short
Equities 0,885 3,625 1,346 -0,608 -0,338 -4,006 0,682 0,533
p-value 0,020 0,362 0,774 0,887 0,896 0,459
Macro 1,341 1,568 -9,002 1,585 7,839 3,918 0,408 0,131
p-value 0,484 0,450 0,714 0,482 0,564 0,890
Multistrategy 1,203 -0,496 4,881 -0,014 0,771 0,769 0,492 0,254
p-value 0,006 0,912 0,362 0,998 0,793 0,900
Relative Value -0,017 0,520 -1,933 -1,297 -1,079 -1,555 0,431 0,165
p-value 0,939 0,833 0,511 0,629 0,506 0,645
Table 7.10 Summarized Multi-Factor results for the entire period, January 2004 – December
2007.
Multi-Factor
Model
Strategies
2008M01 -20012M03
Intercept Beta Beta-
SMB
Beta-
HML Beta-MOM Beta-MT R2
Adj-
R2
Arbitrage 0,065 -1,168 1,284 0,152 -1,186 2,867 0,510 0,300
p-value 0,917 0,493 0,588 0,959 0,415 0,254
CTA 0,223 -0,415 0,598 0,962 -0,547 0,041 0,486 0,265
p-value 0,451 0,605 0,593 0,494 0,425 0,972
Event Driven 0,644 -0,871 2,948 1,415 -2,415 1,454 0,814 0,735
p-value 0,178 0,499 0,106 0,529 0,033 0,442
Fixed Income 0,737 -2,269 1,409 0,248 -1,194 2,625 0,823 0,748
p-value 0,015 0,006 0,204 0,857 0,082 0,028
Long Short
Equities 0,023 -0,263 1,664 0,669 -2,932 1,140 0,859 0,798
p-value 0,948 0,779 0,207 0,683 0,001 0,408
Macro 0,177 -3,999 -1,782 4,511 -2,258 4,951 0,708 0,583
p-value 0,787 0,073 0,527 0,373 0,120 0,049
Multistrategy -0,084 0,158 0,082 -1,431 -2,894 0,775 0,798 0,711
p-value 0,849 0,895 0,961 0,497 0,007 0,661
Relative Value 0,035 -0,896 -0,132 0,614 -0,954 0,604 0,706 0,580
p-value 0,898 0,230 0,898 0,634 0,136 0,578
Table 7.11 Summarized Multi-Factor results for the entire period, January 2008 – March
2012.